Ambitious scenarios of carbon emission redistribution for mitigating climate change in line with the Paris Agreement and reaching the sustainable development goal of eradicating poverty have been proposed recently. They imply a strong reduction in carbon footprint inequality by 2030 that effectively halves the Gini coefficient to about 0.25. This paper examines feasibility of these scenarios by analyzing the historical evolution of both weighted international inequality in CO2 emissions attributed territorially and global inequality in carbon footprints attributed to end consumers. For the latter, a new dataset is constructed that is more comprehensive than existing ones. In both cases, we find a decreasing trend in global inequality, partially attributed to the move of China from the lower to the middle part of the distribution, with footprints more unequal than territorial emissions. These results show that realization of the redistributive scenarios would require an unprecedented reduction in global inequality far below historical levels. Moreover, the territorial emissions data, available for more recent years up to 2017, show a saturation of the decreasing Gini coefficient at a level of 0.5. This observation confirms an earlier prediction based on maximal entropy reasoning that the Lorenz curve converges to the exponential distribution. This saturation further undermines feasibility of the redistributive scenarios, which are also hindered by structural tendencies that reinforce carbon footprint inequality under global capitalism. One way out of this conundrum is a fast decarbonization of the global energy supply in order to decrease global carbon emissions without relying crucially on carbon inequality reduction.